# Question #a7c94

May 24, 2017

The the weight of the balloon is less that that of air, the balloon rises due to the buoyant force.

#### Explanation:

This situation involves the concepts of Archimedes' Principle, stating that "object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object".

In the case of the balloon, there are two things that must be considered:

1. The (total) weight of the balloon.
2. The weight of the air that is displaced when the balloon rises.

The the weight of the balloon is less that that of air, the balloon rises due to the buoyant force.

For example, air is mostly comprised of nitrogen gas (78%) and oxygen gas (21%) and the other 1% includes miscellaneous gases such as argon and carbon dioxide.

For now, we will round nitrogen's percent to 80% and oxygen to 20%. Nitrogen has a molar mass of 28.02 g/mol, while oxygen has a molar mass of 32 g/mol. Therefore, in total, the molar mass of air is 28.816 g/mol.

$\left(28.02 \times 0.8\right) + \left(32.00 \times 0.2\right) = 28.816$

The molar mass of helium is 4 g/mol. As a result, helium is 7.204 times less dense than air.

"If you had a balloon that displaced 7.2 g of air, it would contain 1 g of helium. Thus, the rubber in the balloon could weigh as much as 6.2 g, and the balloon would still float".

Hope this helps :)